automorphisms groups
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2019 ◽  
Vol 35 (4) ◽  
pp. 1153-1194
Author(s):  
Maurício Corrêa ◽  
Alan Muniz

2018 ◽  
Vol 83 (2) ◽  
pp. 395-415
Author(s):  
LOVKUSH AGARWAL ◽  
MICHAEL KOMPATSCHER

AbstractGiven two structures${\cal M}$and${\cal N}$on the same domain, we say that${\cal N}$is a reduct of${\cal M}$if all$\emptyset$-definable relations of${\cal N}$are$\emptyset$-definable in${\cal M}$. In this article the reducts of the Henson digraphs are classified. Henson digraphs are homogeneous countable digraphs that omit some set of finite tournaments. As the Henson digraphs are${\aleph _0}$-categorical, determining their reducts is equivalent to determining the closed supergroupsG≤ Sym(ℕ) of their automorphism groups.A consequence of the classification is that there are${2^{{\aleph _0}}}$pairwise noninterdefinable Henson digraphs which have no proper nontrivial reducts. Taking their automorphisms groups gives a positive answer to a question of Macpherson that asked if there are${2^{{\aleph _0}}}$pairwise nonconjugate maximal-closed subgroups of Sym(ℕ). By the reconstruction results of Rubin, these groups are also nonisomorphic as abstract groups.


2017 ◽  
Vol 9 (2) ◽  
pp. 95
Author(s):  
Andre S. Diabang ◽  
Alassane Diouf ◽  
Mankagna A. Diompy ◽  
Alhousseynou Ba

In this paper, we study partially the automorphisms groups of four-dimensional division algebra. We have proved that there is an equivalence between Der(A)=su(2) and Aut(A)=SO(3). For an unitary four-dimensional real division algebra, there is an equivalence between dim(Der(A))=1 and Aut(A)=SO(2).


2017 ◽  
Vol 230 ◽  
pp. 102-143
Author(s):  
GRZEGORZ GROMADZKI ◽  
SUSUMU HIROSE ◽  
BŁAŻEJ SZEPIETOWSKI

In Hirose (Tohoku Math. J. 62 (2010), 45–53), Susumu Hirose showed that, except for a few cases, the order $N$ of a cyclic group of self-homeomorphisms of a closed orientable topological surface $S_{g}$ of genus $g\geqslant 2$ determines the group up to a topological conjugation, provided that $N\geqslant 3g$. Gromadzki et al. undertook in Bagiński et al. (Collect. Math. 67 (2016), 415–429) a more general problem of topological classification of such group actions for $N>2(g-1)$. In Gromadzki and Szepietowski (Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 110 (2016), 303–320), we considered the analogous problem for closed nonorientable surfaces, and in Gromadzki et al. (Pure Appl. Algebra 220 (2016), 465–481) – the problem of classification of cyclic actions generated by an orientation-reversing self-homeomorphism. The present paper, in which we deal with topological classification of actions on bordered surfaces of finite cyclic groups of order $N>p-1$, where $p$ is the algebraic genus of the surface, completes our project of topological classification of ‘‘large” cyclic actions on compact surfaces. We apply obtained results to solve the problem of uniqueness of the actions realizing the solutions of the so-called minimum genus and maximum order problems for bordered surfaces found in Bujalance et al. (Automorphisms Groups of Compact Bordered Klein Surfaces: A Combinatorial Approach, Lecture Notes in Mathematics 1439, Springer, 1990).


2013 ◽  
Vol 57 ◽  
pp. 61-69 ◽  
Author(s):  
Gabriel Bartolini ◽  
Antonio F. Costa ◽  
Milagros Izquierdo

2007 ◽  
pp. 793-810 ◽  
Author(s):  
Maximiliano Leyton A. ◽  
Rubén Hidalgo

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